Variance Reduction for Estimation of Shapley Effects and Adaptation to Unknown Input Distribution
Variance Reduction for Estimation of Shapley Effects and Adaptation to Unknown Input Distribution
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DOI：
10.1137/18m1234631
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发表时间：
2020-01-01
影响因子：
2
通讯作者：
Depecker, Marine
中科院分区：
文献类型：
--
作者：
Broto, Baptiste;Bachoc, Francois;Depecker, Marine
Shapley效应是全局敏感性指数：它们量化模型中每个输入变量对输出变量的影响。在这项工作中，我们提出了新的估计这些敏感性指数。当输入分布已知时，我们研究[E.宋，B。L.纳尔逊和J. Staum，SIAM/阿萨J.不确定。数量，4（2016），pp. 1060-1083]，并建议一个新的具有较低的方差。然后，当输入的分布是未知的，我们扩展这些估计。我们提供了本文所研究的估计量的渐近性质。我们也适用于这些估计的真实的数据集。
The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is known, we investigate the already existing estimator defined in [E. Song, B. L. Nelson, and J. Staum, SIAM/ASA J. Uncertain. Quantif., 4 (2016), pp. 1060-1083] and suggest a new one with a lower variance. Then, when the distribution of the inputs is unknown, we extend these estimators. We provide asymptotic properties of the estimators studied in this article. We also apply one of these estimators to a real data set.